So: (1) Different classes have different hit dice. (2) Everyone uses d6 dice for hits. (3) Monsters can cleanly add Fighter levels, since they use the same Hit Dice. (4) The DM can roll all monster hit dice with a big handful of regular d6's, instead of having to keep track of a set of d8's just for that purpose. Ah, sweet relief. :)

(Also, an elegant way to roll d6-1: Roll d6's, turn any "6" into a "1". Average is 2.67, compare to d4's average of 2.5.)

So, Anonymous, my instinct says that your method will mean higher hp totals on average than the mine (with the “standard” only-roll-the-new-HD). I’d have to think about it some more to be sure. Is that the case?

Another idea I’ve toyed with is having a 0-level hit die. So, the average 0-level human would have, say, 1d6. PCs would then have the 0-level HD in addition to their class HD. So, a 2nd level fighter would have 3d6+2 (i.e. 1d6 + 2d6+2). A 3rd level mage would have 4d6-3.